Mike Rupp was in his first season with the Devils in 2003 — the one that ended with him scoring the Stanley Cup-winning goal — when he realized the extent of the rivalry with the Rangers.

“I just remember the chants. . . . We were playing the Florida Panthers and (the Devils fans) were chanting “Rangers suck,’” Rupp, who now serves a fourth-line role for the Rangers, said before the Blueshirts won Game 1 of the Eastern Conference finals, 3-0, Monday night at the Garden. “That’s the one thing I remember thinking: ‘Wow, there must be something to this. It’s obviously something special.’

“But right now, at this point in the playoffs, I think that’s more for the fans and the media to have fun with. For us, it’s about going out there and winning four games.”

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Rupp, 32, actually has connections to all three local teams. He was a top-10 pick of the Islanders in 1998, but the hulking winger didn’t sign with them and re-entered the draft, only to be selected by the Devils in the third round of 2000.

Rupp served two tours of duty with Jersey — with stops in Phoenix and Columbus in between — before two productive seasons in Pittsburgh (22 goals and 244 penalty minutes) landed him a three-year, $4.5 million contract to fill a tough-guy role with the Rangers last summer.

“It’s good for the game, it’s good for the fans, this series and the buzz around here,” Rupp said of the first Rangers-Devils series since 2008. “We know the Knicks are done. These are teams that are close to each other, that don’t like each other.”

Rupp, of course, took part in the three-fight brawl just after the opening faceoff that marred the game between the teams on March 19. But he expects little, if any, carryover from that unsightly incident.

“Those are just kind of moments that happened, but right now, it’s a lot bigger than rivalries,” Rupp said. “I think we’re at a stage in the season right now in the playoffs where we need to take the next step, and both teams probably feel the same way.

“We’re going to go out there and do our thing. It’s not like all of a sudden, because it’s New Jersey, that we’re going to play harder or play better. I’d like to think we’d play the same if it was anybody. So I don’t really think about it right now. Maybe in the early parts of the playoffs you would, but not now.”

Rupp, the only player in Stanley Cup history to have his first career playoff goal be the Cup-winner, also said the Devils have become more of an offensive team under first-year coach Pete DeBoer than those he played on from 2002-04 and 2007-09.

“Right now, you’re four wins away from getting to where you’ve been working so hard to get to as a team, so I don’t really think about any of that,” Rupp said. “I really don’t. I don’t look at it like me once playing for them or them being our biggest rivals, that’s kind of non-existent right now. Right now it’s about winning hockey games, it doesn’t matter who it’s against.”